Lab 7: IQ Sample-Rate Exploration

Chapter: 7 (Week 8) Duration: 3.5 hr Substrate: ANTSDR E200 (physical); virtual path: lab7-2msps.iq + lab7-8msps.iq + lab7-20msps.iq Points: 10

Overview

Capture the same 433.92 MHz OOK signal at three different sample rates (2/8/20 MSPS) and analyse the spectral and temporal differences. Observe: spectral resolution, noise floor, dynamic range, and neighbouring-signal visibility. Connect observations to the Wyglinski IQ-sampling theory from Week 8.

Part 1: Capture Setup (45 min)

Physical path (ANTSDR E200)

Configure three sequential captures of the same ISM-band signal source. Use a known signal source: a 433.92 MHz OOK temperature sensor (or the instructor-provided lab signal source at 433.92 MHz).

GNU Radio capture flowgraph:

[PlutoSDR Source]
  URI: ip:192.168.1.10
  Center Freq: 433.92e6
  Sample Rate: (varies: 2e6 / 8e6 / 20e6)
  RF Bandwidth: (varies: same as sample rate)
  Gain: Manual, 40 dB
      |
   [File Sink: lab7-Nmsps.iq]
      |
   [QT GUI Frequency Sink]

Run each for 15 seconds. You will have three files: lab7-2msps.iq, lab7-8msps.iq, lab7-20msps.iq.

Virtual path

Use the provided three IQ archive files. They were captured from a 433.92 MHz OOK temperature sensor at the three sample rates.

Part 2: Spectrum Comparison (60 min)

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import welch

def spectrum_analysis(filename, fs, label, colour):
    samples = np.fromfile(filename, dtype=np.complex64)
    # Use Welch's method for a smoother power spectrum estimate
    N_seg = min(len(samples), 8192)
    freqs, psd = welch(samples, fs=fs, nperseg=N_seg, return_onesided=False)
    freqs = np.fft.fftshift(freqs)
    psd_db = 10 * np.log10(np.fft.fftshift(psd) + 1e-15)
    plt.plot(freqs / 1e3, psd_db, label=label, color=colour, alpha=0.8, linewidth=0.8)

plt.figure(figsize=(14, 7))
spectrum_analysis("lab7-2msps.iq",  2e6,  "2 MSPS",  'blue')
spectrum_analysis("lab7-8msps.iq",  8e6,  "8 MSPS",  'orange')
spectrum_analysis("lab7-20msps.iq", 20e6, "20 MSPS", 'green')
plt.xlabel("Frequency offset from centre (kHz)")
plt.ylabel("Power spectral density (dB/Hz)")
plt.title("433.92 MHz OOK sensor at three sample rates")
plt.legend(); plt.grid(True, alpha=0.4)
plt.xlim(-10000, 10000)  # ±10 MHz view
plt.tight_layout(); plt.show()

From the plot, answer:

1. What is the noise floor (dBm/Hz) for each sample rate? (Look at the flat portions of the PSD away from the signal)
2. The noise floor shifts as sample rate increases. By approximately how many dB between 2 MSPS and 20 MSPS? What is the theoretical prediction (thermal noise power = kTB; doubling bandwidth = +3 dB noise)?
3. At 20 MSPS, are there any signals visible in the spectrum besides the target 433.92 MHz source? Identify and describe them (hint: adjacent ISM devices, harmonics, or interference).
4. At 2 MSPS, how wide is the target OOK signal's occupied bandwidth (the −3 dB and −20 dB bandwidth)?

Part 3: Time-Domain Analysis (45 min)

Look at the OOK pulse structure in the time domain.

import numpy as np
import matplotlib.pyplot as plt

def time_analysis(filename, fs, label):
    samples = np.fromfile(filename, dtype=np.complex64)
    envelope = np.abs(samples[:50000])
    t = np.arange(len(envelope)) / fs * 1e3  # time in ms
    plt.figure(figsize=(14, 3))
    plt.plot(t, envelope, linewidth=0.4)
    plt.xlabel("Time (ms)"); plt.ylabel("Amplitude")
    plt.title(f"OOK envelope: {label} (first 50,000 samples)")
    plt.grid(True, alpha=0.3); plt.tight_layout(); plt.show()

time_analysis("lab7-2msps.iq",  2e6,  "2 MSPS")
time_analysis("lab7-8msps.iq",  8e6,  "8 MSPS")
time_analysis("lab7-20msps.iq", 20e6, "20 MSPS")

From the three plots:

1. What is the approximate symbol period (in milliseconds) of the OOK signal?
2. At which sample rate is it easiest to see individual bit transitions? Why? (More samples per symbol = more time-domain resolution)
3. At 20 MSPS, how many samples represent one symbol period? (samples_per_symbol = fs × T_symbol)

Part 4: Dynamic Range Measurement (30 min)

import numpy as np

def measure_dynamic_range(filename, fs):
    samples = np.fromfile(filename, dtype=np.complex64)
    envelope = np.abs(samples)
    # Signal peak (dBFS)
    peak = 20 * np.log10(envelope.max())
    # Noise floor estimate: median of the lowest 10% of samples (silence periods)
    sorted_env = np.sort(envelope)
    noise_floor_lin = np.median(sorted_env[:len(sorted_env)//10])
    noise_floor_db = 20 * np.log10(noise_floor_lin + 1e-9)
    dynamic_range = peak - noise_floor_db
    print(f"  Peak: {peak:.1f} dBFS   Noise floor: {noise_floor_db:.1f} dBFS   DR: {dynamic_range:.1f} dB")

print("2 MSPS:"); measure_dynamic_range("lab7-2msps.iq",  2e6)
print("8 MSPS:"); measure_dynamic_range("lab7-8msps.iq",  8e6)
print("20 MSPS:"); measure_dynamic_range("lab7-20msps.iq", 20e6)

Theoretical prediction check: The noise floor should rise by 10×log10(fs_new/fs_old) dB when sample rate increases (wider bandwidth admits more noise power). Does the measured shift match the theory?

Part 5: Sample-Rate Choice Analysis (30 min)

Write a 1-paragraph analysis: for capturing and demodulating this specific OOK ISM protocol, which sample rate would you choose in a real deployment and why? Your answer must address:

• Symbol resolution (samples per symbol at each rate)
• Noise floor (wider bandwidth = more noise)
• Spectrum visibility (ability to see adjacent channels)
• Storage cost (file size per unit time at each rate)
• Aliasing risk (are any nearby signals aliased in at any rate?)

Deliverables

• Spectrum comparison plot (all three sample rates on one figure)
• Three time-domain envelope plots (one per sample rate)
• Dynamic-range measurements (Python output, Part 4)
• Written answers to all analysis questions (Parts 2, 3, 4)
• Sample-rate choice analysis paragraph (Part 5)

Grading (10 points)